To answer your immediate question, the noise will probably be more annoying to her than will be the recoil. Put her in both, some soft foam plugs as well as a good set of muffs and she should do fine with either. The thing I have found with kids is they relate to the noise levels more than recoil, at least with the ones I have gotten into shooting. The louder it is the more they think it will kick. I have a short barrel .308 which is a loud little critter, but recoil is not bad at all, and my nephew would rather shoot the 7 mag over it simply due to how loud it was to him. He just couldn't get it, that the recoil wasn't as bad as it sounded.
My daughter started out at 6 and her son at 3.5 shooting with me. Their choices not me pushing them into it. The biggest thing to them was being out there hunting not what they were shooting. The grandson did take reducing the loads for my compact .308 down, but he dropped his first feral hog in it's tracks at 50 yds just before his 5th birthday. The daughter got her first deer with my 25 just before her 9th.
If they are interested in it they will adjust and accept what the rifle does when the trigger is pulled. Just start out with a few rounds at a sitting like 3-5 and adjust to more as they want. You will find in most cases after the first few sittings they will ask if they can shoot more. I would let them shoot the .22 for a few rounds to get their trigger finger ready and then move into the high power stuff, then back to the .22 for more trigger work. After a few outings they weren't interested much in the .22 anymore.
Good luck with your daughter, it is a great thing to pass along the shooting and hunting skills and be by their side when the moment comes for them to become hunters. Just don't push them into it and they seem to fall right in. Above all however, when hunting, it is always about being out there in the outdoors enjoying the wild life and God's creations over the kill, and even the lowliest spike buck or doe, is a trophy, depending on the circumstances of the hunt. Never make it out to be, the biggest has to be the best, or they will get tired of waiting for the ones they see on TV and will probably never see.